Lower back pain is a common symptom of kidney problems. Other symptoms, however, usually accompany kidney failure - such as high blood pressure, headaches, increase fatigue, etc. You may visit the following website for more details: http://www.comprehensive-kidney-facts.com/kidney-failure-symptoms.html
Kidney stones can also contribute to pain in the lower back. Depending on the size and location of the stone, pain can range from mild to severe and may extend to the side, or in the groin area (extending to the inner thighs). You can learn more about this from this web page: http://www.comprehensive-kidney-facts.com/kidney-stones.html
You should not, however, automatically assume that pain in the mid to lower back is as a result of kidney problems. It could also be as a result of muscle spasms (as I experienced a few years ago). Muscle spasms usually causes pain accompanied by tightness (caused by contraction of the muscles)... which is similar to what you described.
If the pain persist for more than a few days I will advise you to visit your doctor to have to problem diagnosed. In the interim, continue to drink lots of water every day. Cut back on the consumption of sugars, red meats, dairy products and highly refined foods and snacks, and include more fruits and vegetables in your diet.
Wishing you all the best and hope that the pain will soon be gone.